**A right triangle has 20 inches long hypotenuse. Prove that the triangle is an isosceles triangle with maximum perimeter**

**Answer:**

In a simple example, leg 1 and leg 2 are set congruent at a side length of 1 and their base angles are 45 degrees each. The hypotenuse can be calculated using the Pythagorean Theorem because 1^2+1^2=c^2 (c is hypotenuse) will give you what you need to start with. 1^2=1, so both a and b are solved in 1 step. 1+1=2=c^2. Solve by finding the square root of 2. The square root of 2 is the answer for the length of the hypotenuse.

Now, reverse engineer the question. Set up a proportion. (Square root of 2)/1=20/x

Cross-multiply 1x20 to get 20 and divide by the 2. The answer isnâ€™t pretty, but one leg length is 14.14213562 (rounded off to 10 significant digits). Add the 20, 14.14 (approx.) and 14.14 to get a perimeter of 48.28427124 and maybe round if your teacher wants that.

Anyway, Perimeter=48.28427124 u